Problem 4 (Provision of Public Good) There are two major owners of real estate in Shorewood Hills area in Madison, WI, called Alfon Inc (A) and Beton Inc. (B). Both firms specialize in renting their apartments to UW faculty. Each year firm A and firm B decides how much to spend on the common areas in Shorewood Hills, such us playgrounds and bike paths. x and x are spendings for Alfon and Beton respectively and x = x + x# is the total spending for both firms. The common area is used by all members of the community, and hence x is non-excludable. The market rent received by firm A depends on the quality of the property and its surrounding common area. The profit then is given by: TA = In(x4 + xB)- x The customers of firm B value the common area more hence the profit of firm B is given by: nB = 2In(x4 + xB)- xB a) suppose x= 0.5. Find the optimal level of investment in a common area by firm A, x4. Mark this point in space (x4,xB). b) Find analytically the best response function for firm A (an optimal investment x as a function of x#) and plot the entire function in your graph from a) Make sure you also show the optimal x for x8 > 1. c) Find the best response function for firm B. Add it to the graph. d) Find in your graph the (Nash) equilibrium for two firms (x*4,x*#). What is the total amount of money invested in common area? e) Is the predicted outcome associated with free riding? If yes by which firm? Explain why this firm is free riding? f) What is the Pareto efficient joint level of investment in the common area? Is it greater, smaller or equal to the one observed in the market (point d)? Explain intuitively why is it so